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We say that a surface in Minkowski 3-space is a lightlike developable if all pseudo-normal vectors of the regular part of the surface sire lightlike. The tangent surface of a lightlike curve is one of the lightlike developables. We give a generic classification of such surfaces. The all arguments in this paper are elementary. However, we discovered the H3 type singularity appears in generic for such a class of surfaces. Since the H3 type singularity usually appears in non-generic situation,doi:10.1515/dema-2010-0212 fatcat:jkoifrd4tjbm3b3bujjfxdj7na